instance generators, and developed several algorithms with theoretical and practical guarantees. We
have also continuously developed tools to share
experimental instance data, results, and solution
visualizations with our collaborators throughout (Le
Bras et al. 2011; Ermon et al. 2012; Le Bras et al. 2014;
Ermon et al. 2015; Xue et al. 2015). Phase-Mapper is
our most successful tool to date in this area: it
removes many of the practical barriers to the use of
previous methods, including better scalability, run-times suitable for interactive use, and ease of access.

Phase-Mapper has been used at the Department of
Energy’s Joint Center for Artificial Photosynthesis
(JCAP) to run hundreds of phase-mapping solutions
in the JCAP materials discovery pipeline. Prior to
Phase-Mapper, the difficulty of interpreting X-ray diffraction data limited JCAP scientists’ ability to take
full advantage of resources to conduct high-throughput experiments. Since the deployment of Phase-Mapper, thousands of X-ray diffraction patterns have
been processed and the results are yielding discovery
of new materials for energy applications. These are
exemplified by the discovery of a new family of metal oxide light absorbers in the previously unsolved
Nb-Mn-V oxide system, which is provided here as a
case study and is an illustrative example of the
importance of encoding physical constraints to
obtain physically meaningful phase diagram solutions. We believe Phase-Mapper will lead to further
developments in high-throughput materials discovery by providing rapid and critical insights into the
phase behavior of new materials.

Phase-Mapper: AI forMaterials DiscoveryAn experimentation pipeline for rapidly synthesiz-ing, characterizing, and identifying new materials isreferred to as high-throughput materials discovery orcombinatorial materials discovery. In this pipeline, ahandful of elements are deposited together on a two-dimensional substrate, so that different locations onthe substrate receive varying proportions of the ele-ments. This smooth variation in elemental composi-tion across the substrate gives rise to the forming ofa discrete set of materials, each of which is present inparticular regions of the substrate.

The deposition process is analogous to atomicspray paint, as mentioned earlier. Imagine red, green,and blue spray paint being simultaneously sprayedonto a surface (or wafer) with each color sourceplaced at the vertex of an equilateral triangle. Nearthese vertices, the deposited color appears simplyred, green, or blue, and throughout the area of thetriangle a continuum of the possible colors areobtained, where each color on the spectrum exists ata unique point on the wafer. In the same manner, thedeposited materials “library” contains a broad spec-trum of compositions (given the starting elements),and the atoms in different composition regions mayarrange in a unique way to form a unique “phase”whose properties differ from other materials, evenother compositions and phases formed from thesame elements. It is the hope that one of these newmaterials will have a composition and phase thatexhibit the desired properties, and to fully under-stand the composition-phase-property relationships,the full phase map must be solved.In the libraries being studied, the new materials aretypically crystalline, meaning that at the atomic scaleatoms are arranged in particular lattice structures,and the phase noted earlier is described by the sym-metry and composition of the lattice structure. On alarger length scale, typically 5 to 500 nm, the latticestructure may alternate between two or three differ-ent structures, constituting a mixed-phase material.Each phase and phase mixture can exhibit uniqueproperties, creating the need for materials scientiststo understand, for each material library, how to cate-gorize each material in the library (on the wafer) interm of its phase mixtureWhat data should materials scientists look at todetermine the crystal structures? An indirect way ofprobing the microscopic structure is through X-raydiffraction. When X-rays are directed against a crys-tal, atomic layers will reflect the light; and for specificangles determined by the spacing between atomiclayers, this reflected light will interfere constructive-ly, giving rise to a strong signal. Thus, by scanningthrough all angles and measuring the reflected light,materials scientists are able to infer the structure ofFigure 1. The Phase-Mapper Platform.